If he is trying to rp for the pact of the blade to explain how he receives his weapon, you could always dream sequence it. Have him do some lucid dreaming type thing where his patron leads him to or gives him his blade. When he wakes up he realizes he can summon it and bam problem solved without long party detour. Patrons work in mysterious ways after all.
And the idea I'm running with for this campaign involves my players tracking down a series of magical weapons.
So imagine my displeasure when my Warlock (3 sessions in) pulls me aside to tell me that he has to track down a magic weapon for his whole Warlock quest thing.
So his quest is to do what the quest was going to be anyway?
The warlock's level 3 feature Pact of the Blade doesn't require a specific weapon to be found or possessed, the patron bestows upon you the ability to create a pact weapon out of nothing. But if you wanted to tie it in with the quest you had planned, just make it so that the warlock doesn't actually receive his level 3 pact boon before he's found one of these weapons, so that he can siphon off a miniscule amount of it's power in a ritual to please the patron and be rewarded with the pact boon.
Yeah, like @Twooshort was saying, you don't necessarily need to have a quest, or a sidequest specifically for the warlock's Pact. The Power required could be a number of things that fit into his Patron's pleasures. have him do a ritual requiring a sacrifice of some sort (whether that be gold or animals, or a curse for a blessing) that allows the patron to give him the Magic necessary to imbue a blade with the Pact.
you don't have to have an already "magical" weapon for the Blade Pact to function. The Pact is what makes the blade specifically attuned to the Patron, and the Warlock has access to the Patron's magic through that attunement, if that makes sense.
I'm not sure why the player is telling the DM what mission he needs to do. His input is only a suggestion. There are no classes in 5e that require roleplaying milestones to progress (although there were some in UA, they never implemented them).
Like everyone else has said, I think you or he is misunderstanding something.
@LuckyTab Thank you for that suggestion because that's exactly what he wanted to do, and I ended up doing something relatively similar which worked wonderfully. I ended up sitting down with him properly and talking details out before we did a small side-session and did that whole deal!